交替最小化与随机最小化的相位恢复
Phase Retrieval by Alternating Minimization with Random Initialization
摘要：
我们考虑一个相位恢复问题，其目标是重建一个$n$维复向量从其无相位标量产品与$m$感测向量，独立地从复杂的正态分布采样。我们表明，与随机初始化，交替最小化的经典算法成功与$n,m\rightarrow\infty$高概率时，${m}/{\log^3m}\geq Mn^{3/2}\log^{1/2}n$的一些$M>0$。这是证明\cite{Waldspurger2016}中的猜想的一步，它证明了当$m=O(n)$。该分析依赖于一种方法，该方法能够解耦算法迭代和感测向量之间的依赖关系。
英文摘要：
We consider a phase retrieval problem, where the goal is to reconstruct a $n$-dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that, with a random initialization, the classical algorithm of alternating minimization succeeds with high probability as $n,m\rightarrow\infty$ when ${m}/{\log^3m}\geq Mn^{3/2}\log^{1/2}n$ for some $M>0$. This is a step toward proving the conjecture in \cite{Waldspurger2016}, which conjectures that the algorithm succeeds when $m=O(n)$. The analysis depends on an approach that enables the decoupling of the dependency between the algorithmic iterates and the sensing vectors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
